Why was Charles Fourier important?
To the extent that Charles Fourier is important, it is because he was a utopian socialist thinker in the late 1700s and early 1800s. He was responding to the changes in society that were brought about by industrialization and capitalism. Fourier's thinking did not really change the world in that it was not adopted by any governments. However, it did have a major influence on thinkers of his time, people like Feodor Dostoevsky and the Transcendentalists of the United States.
Fourier believed that industrialization was making people bored and selfish. He advocated changing this by creating communities that he called "phalanxes." In these communities, people would change jobs often and change sexual partners as well so as to help themselves avoid becoming bored and selfish. This ideal community of his is described at much greater length in the link below.
Fourier, then, was important as a thinker who had ideas that would, he thought, take care of the problems brought on by the move towards industrialization and capitalism.